An official website of the United States government
Abstract Number sense is fundamental to the development of numerical problem‐solving skills. In early childhood, children establish associations between non‐symbolic (e.g., a set of dots) and symbolic (e.g., Arabic numerals) representations of quantity. The developmental estrangement theory proposes that the relationship between non‐symbolic and symbolic representations of quantity evolves with age, with increased dissociation across development. Consistent with this theory, recent research suggests that cross‐format neural representational similarity (NRS) between non‐symbolic and symbolic quantities is correlated with arithmetic fluency in children but not in adolescents. However, it is not known if short‐term training (STT) can induce similar changes as long‐term development. In this study, children aged 7–10 years underwent a theoretically motivated 4‐week number sense training. Using multivariate neural pattern analysis, we investigated whether short‐term learning could modify the relation between cross‐format NRS and arithmetic skills. Our results revealed a significant correlation between cross‐format NRS and arithmetic fluency in distributed brain regions, including the parietal and prefrontal cortices, prior to training. However, this association was no longer observed after training, and multivariate predictive models confirmed these findings. Our findings provide evidence that intensive STT during early childhood can promote behavioral improvements and neural plasticity that resemble and recapitulate long‐term neurodevelopmental changes that occur from childhood to adolescence. More generally, our study contributes to our understanding of the malleability of number sense and highlights the potential for targeted interventions to shape neurodevelopmental trajectories in early childhood. Research HighlightsWe tested the hypothesis that short‐term number sense training induces the dissociation of symbolic numbers from non‐symbolic representations of quantity in children.We leveraged a theoretically motivated intervention and multivariate pattern analysis to determine training‐induced neurocognitive changes in the relation between number sense and arithmetic problem‐solving skills.Neural representational similarity between non‐symbolic and symbolic quantity representations was correlated with arithmetic skills before training but not after training.Short‐term training recapitulates long‐term neurodevelopmental changes associated with numerical problem‐solving from childhood to adolescence.
more »
« less
Learning-induced reorganization of number neurons and emergence of numerical representations in a biologically inspired neural network
Abstract Number sense, the ability to decipher quantity, forms the foundation for mathematical cognition. How number sense emerges with learning is, however, not known. Here we use a biologically-inspired neural architecture comprising cortical layers V1, V2, V3, and intraparietal sulcus (IPS) to investigate how neural representations change with numerosity training. Learning dramatically reorganized neuronal tuning properties at both the single unit and population levels, resulting in the emergence of sharply-tuned representations of numerosity in the IPS layer. Ablation analysis revealed that spontaneous number neurons observed prior to learning were not critical to formation of number representations post-learning. Crucially, multidimensional scaling of population responses revealed the emergence of absolute and relative magnitude representations of quantity, including mid-point anchoring. These learnt representations may underlie changes from logarithmic to cyclic and linear mental number lines that are characteristic of number sense development in humans. Our findings elucidate mechanisms by which learning builds novel representations supporting number sense.
more »
« less
- Award ID(s):
- 2024856
- PAR ID:
- 10441267
- Date Published:
- Journal Name:
- Nature Communications
- Volume:
- 14
- Issue:
- 1
- ISSN:
- 2041-1723
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Many species of animals exhibit an intuitive sense of number, suggesting a fundamental neural mechanism for representing numerosity in a visual scene. Recent empirical studies demonstrate that early feedforward visual responses are sensitive to numerosity of a dot array but substantially less so to continuous dimensions orthogonal to numerosity, such as size and spacing of the dots. However, the mechanisms that extract numerosity are unknown. Here, we identified the core neurocomputational principles underlying these effects: (1) center-surround contrast filters; (2) at different spatial scales; with (3) divisive normalization across network units. In an untrained computational model, these principles eliminated sensitivity to size and spacing, making numerosity the main determinant of the neuronal response magnitude. Moreover, a model implementation of these principles explained both well-known and relatively novel illusions of numerosity perception across space and time. This supports the conclusion that the neural structures and feedforward processes that encode numerosity naturally produce visual illusions of numerosity. Taken together, these results identify a set of neurocomputational properties that gives rise to the ubiquity of the number sense in the animal kingdom.more » « less
-
Abstract Numerosity perception is largely governed by two mechanisms. The first so-called subitizing system allows one to enumerate a small number of items (up to three or four) without error. The second system allows only an approximate estimation of larger numerosities. Here, we investigate the neural bases of the two systems using sequentially presented numerosity. Sequential numerosity (i.e., the number of events presented over time) starts as a subitizable set but may eventually transition into a larger numerosity in the approximate estimation range, thus offering a unique opportunity to investigate the neural signature of that transition point, or subitizing boundary. If sequential numerosity is encoded by two distinct perceptual mechanisms (i.e., for subitizing and approximate estimation), neural representations of the sequentially presented items crossing the subitizing boundary should be sharply distinguishable. In contrast, if sequential numerosity is encoded by a single perceptual mechanism for all numerosities and subitizing is achieved through an external postperceptual mechanism, no such differences in the neural representations should indicate the subitizing boundary. Using the high temporal resolution of the EEG technique incorporating a multivariate decoding analysis, we found results consistent with the latter hypothesis: No sharp representational distinctions were observed between items across the subitizing boundary, which is in contrast with the behavioral pattern of subitizing. The results support a single perceptual mechanism encoding sequential numerosities, whereas subitizing may be supported by a postperceptual attentional mechanism operating at a later processing stage.more » « less
-
Attractive serial dependence refers to an adaptive change in the representation of sensory information, whereby a current stimulus appears to be similar to a previous one. The nature of this phenomenon is controversial, however, as serial dependence could arise from biased perceptual representations or from biased traces of working memory representation at a decisional stage. Here, we demonstrated a neural signature of serial dependence in numerosity perception emerging early in the visual processing stream even in the absence of an explicit task. Furthermore, a psychophysical experiment revealed that numerosity perception is biased by a previously presented stimulus in an attractive way, not by repulsive adaptation. These results suggest that serial dependence is a perceptual phenomenon starting from early levels of visual processing and occurring independently from a decision process, which is consistent with the view that these biases smooth out noise from neural signals to establish perceptual continuity.more » « less
-
Number sense is essential for early mathematical development but it is compromised in children with mathematical disabilities (MD). Here we investigate the impact of a personalized 4-week Integrated Number Sense (INS) tutoring program aimed at improving the connection between nonsymbolic (sets of objects) and symbolic (Arabic numerals) representations in children with MD. Utilizing neural pattern analysis, we found that INS tutoring not only improved cross-format mapping but also significantly boosted arithmetic fluency in children with MD. Critically, the tutoring normalized previously low levels of cross-format neural representations in these children to pre-tutoring levels observed in typically developing, especially in key brain regions associated with numerical cognition. Moreover, we identified distinct, ‘inverted U-shaped’ neurodevelopmental changes in the MD group, suggesting unique neural plasticity during mathematical skill development. Our findings highlight the effectiveness of targeted INS tutoring for remediating numerical deficits in MD, and offer a foundation for developing evidence-based educational interventions. Significance StatementFocusing on neural mechanisms, our study advances understanding of how numerical problem-solving can be enhanced in children with mathematical disabilities (MD). We evaluated an integrated number sense tutoring program designed to enhance connections between concrete (e.g. 2 dots) and symbolic (e.g. “2”) numerical representations. Remarkably, the tutoring program not only improved these children’s ability to process numbers similarly across formats but also enhanced their arithmetic skills, indicating transfer of learning to related domains. Importantly, tutoring normalized brain processing patterns in children with MD to resemble those of typically developing peers. These insights highlight the neural bases of successful interventions for MD, offering a foundation for developing targeted educational strategies that could markedly improve learning outcomes for children facing these challenges.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1038/s41467-023-39548-5
